In strongly disordered matter, such as liquids and glasses, atomic and magnetic excitations are heavily damped and partially localized by disorder. Thus, the conventional descriptions in terms of phonons and magnons are inadequate, and we have to con...
Boundedness is an essential feature of the solutions for various mathematical and numerical models in the natural sciences, especially those systems in which linear or nonlinear preservation or stability features are fundamental. In those cases, the...
The main purpose of this work is to study how loss functions in machine learning influence the “binary machines”, i.e., probabilistic AI models for predicting binary classification problems. In particular, we show the following results: (...
The interacting quantum atoms approach (IQA) as applied to the electron-pair exhaustive partition of real space induced by the electron localization function (ELF) is used to examine candidate energetic descriptors to rationalize substituent effects...
In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex func...
This work presents an investigation to model chemical bonding in various dimers based on the atomic fragment approach. The atomic fragment approach is an ab-initio, parameter-free implementation of orbital-free density functional theory which is base...
This work presents a method to move beyond the recently introduced atomic fragment approximation. Like the bare atomic fragment approach, the new method is an ab initio, parameter-free, orbital-free implementation of density functional theory based o...
In this study, we focus on the newly introduced concept of LR-convex interval-valued functions to establish new variants of the Hermite–Hadamard (H-H) type and Pachpatte type inequalities for Riemann–Liouville fractional integrals. By pre...
The main goal of this article is to provide estimates of mild solutions of Navier–Stokes equations with arbitrary external forces in
In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equa...
In this study, Ostrowski-type inequalities in fuzzy settings were investigated. A detailed theory of fuzzy analysis is provided and utilized to establish the Ostrowski-type inequality in the fuzzy number-valued space. The results obtained in this res...
We consider a data-driven method, which combines Koopman operator theory with Extended Dynamic Mode Decomposition. We apply this method to the hypergeometric equation which is the Fuchsian equation with three regular singular points. The space of sol...
In this article, we consider an iterated functions system on the non-Euclidean real projective plane which has a linear structure. Then, we study the fractal dimension of the associated curve as a subset of the projective space and like a set of the...
Generally, the linear topological spaces successfully generate Tychonoff product topology in lower dimensions. This paper proposes the construction and analysis of a multidimensional topological space based on the Cartesian product of complex and rea...
High-quality atomic models providing structural information are the results of their refinement versus diffraction data (reciprocal-space refinement), or versus experimental or experimentally based maps (real-space refinement). A proper real-space re...
The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function
Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as...
The aim of the paper is to introduce the Banach space consisting of real functions defined on a locally compact and countable at infinity metric space and having increments tempered by a modulus of continuity. We are going to provide a condition that...
This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and
A Schauder basis in a real or complex Banach space X is a sequence
The extension of the concept of p-summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space M afforded by t...
In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we cre...
In this paper, we present Proinov-type fixed point theorems in the setting of bi-polar metric spaces and fuzzy bi-polar metric spaces. Fuzzy bi-polar metric spaces with symmetric property extend classical metric spaces to address dual structures and...
We introduce Kuelbs–Steadman-type spaces (
Assessing a built environment’s functional performance and physical and psychological impact is essential for understanding its effect on users, particularly in higher education, where it informs the creation of effective learning spaces. This...
Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated by the exp...
In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous fun...
This work develops an analytical framework for the Hartley transform, which, unlike the Fourier transform, converts real-valued functions into real-valued functions. We derive Parseval–Goldstein-type identities for suitable classes of functions...
As robots become increasingly common in human-populated environments, they must be perceived as social beings and behave socially. People try to preserve their own space during social interactions with others, and this space depends on a variety of f...
In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructin...
In this paper, we study Amari’s natural gradient flows of real functions defined on the densities belonging to an exponential family on a finite sample space. Our main example is the minimization of the expected value of a real function defined on th...
We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in
A holomorphically fibred space generates locally trivial bundles with positive dimensional fibers. This paper proposes two varieties of fibrations (compact and non-compact) in the non-uniformly scalable quasinormed topological (C, R) space admitting...
In general, the state of a system in which a physical quantity such as mass is distributed over space can be modeled by a function that represents the density distribution. The purpose of this paper is to introduce special functions that can be appli...
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebra...
The classical Rolle’s theorem establishes the existence of (at least) one zero of the derivative of a continuous one-variable function on a compact interval in the real line, which attains the same value at the extremes, and it is differentiabl...
This paper provides two new Velichko-like theorems for the weak counterpart of the locally convex space
The representation of electronic wavefunctions in real space grids, which are directly related to molecular orbitals and electronic densities either in molecular or crystalline systems, is a fundamental part of many studies at ab initio levels, since...
The framework of Functional Analysis is the theory of topological vector spaces over the real or complex field. The natural generalization of these objects are the topological modules over topological rings. Weakening the classical Functional Analysi...
In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic alge...
We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies
In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and...
This paper explains why the critical line sits at the real part equal to one-half by treating it as an intrinsic boundary of a reparametrized complex plane (“
The linking (in terms of functional use) of brownfield sites with creative spaces is a frequently encountered phenomenon in western European, post-communist, and industrialized countries in general and is viewed as a way of revitalizing, repurposing,...
In this paper, we explore the Hyers–Ulam stability of a generalized Drygas functional equation, which extends the classical Drygas equation by incorporating additional parameters and conditions. Our investigation focuses on mappings from a real...
Reinforcement learning is one of the most promising machine learning techniques to get intelligent behaviors for embodied agents in simulations. The output of the classic Temporal Difference family of Reinforcement Learning algorithms adopts the form...
In this paper we investigate Hyers-Ulam-Rassias stability of certain nonlinear functional equations. Considerations of such stabilities in different branches of mathematics have been very extensive. Again the fuzzy concepts along with their several e...
Basic neural network operators are interpreted as positive linear operators and the related general theory applies to them. These operators are induced by a symmetrized density function deriving from the parametrized and deformed hyperbolic tangent a...
One of the methods for studying the solvability of infinite systems of integral or differential equations is the application of various fixed-point theorems to operators acting in appropriate functional Banach spaces. This method is fairly well devel...
In this paper, the real-time joint stiffness configuration strategy of a series parallel hybrid 7-DOF (degree of freedom) humanoid manipulator with flexible joints in continuous motion is studied. Firstly, considering the potential human robot accide...
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